Question

Triangle PQR is similar to Triangle XYZ. What is the perimeter of Triangle XYZ?

Answer 1

`\cfrac{PQ}{XY}=\cfrac{QR}{YZ}\implies \cfrac{5}{30}=\cfrac{6}{YZ}\implies 5YZ=180\implies YZ=\cfrac{180}{5}\implies YZ=36 \\\\\\ \cfrac{PQ}{XY}=\cfrac{PR}{XZ}\implies\cfrac{5}{30}=\cfrac{10}{XZ}\implies 5XZ=300\implies XZ=\cfrac{300}{5}\implies XZ=60 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Perimeter of }XYZ}{30~~ + ~~36~~ + ~~60}\implies \text{\LARGE 126}`